Abstract

This paper deals with the asymptotic and oscillatory properties of solutions of a class of second order non-linear damped neutral difference equations of the form D [r(n)(Dz(n))a] + a(n + 1)(Dz(n + 1))a + q(n) f (x(n + s)) = 0; n  n0, () where z(n) = x(n)

where is a ratio of positive odd integers, , and are sequences of real numbers, and are integers, and is a real valued continuous function. We established some new sufficient conditions under which every solution of is either oscillatory or tends to zero as . The results are illustrated with examples.

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